A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to monitor the lithographic process, parameters of the patterned substrate are measured. Parameters may include, for example, the overlay error between successive layers formed in or on the patterned substrate and critical linewidth of developed photosensitive resist. This measurement may be performed on a product substrate and/or on a dedicated metrology target. There are various techniques for making measurements of the microscopic structures formed in lithographic processes, including the use of scanning electron microscopes and various specialized tools. A fast and non-invasive form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. By comparing the properties of the beam before and after it has been reflected or scattered by the substrate, the properties of the substrate can be determined. This can be done, for example, by comparing the reflected beam with data stored in a library of known measurements associated with known substrate properties. Two main types of scatterometer are known. Spectroscopic scatterometers direct a broadband radiation beam onto the substrate and measure the spectrum (intensity as a function of wavelength) of the radiation scattered into a particular narrow angular range. Angularly resolved scatterometers use a monochromatic radiation beam and measure the intensity of the scattered radiation as a function of angle.
As the semiconductor industry still follows the Moore's Law the smallest feature-size, the so-called Critical Dimension (CD), of new-generation integrated circuits (ICs) is continuously shrinking Every next generation (so-called node) of lithography processes is facing even more difficult challenges than the previous one, an important example being so-called Line Edge Roughness (LER). For the nodes below 100 nm the edges of lithography-fabricated IC structures can no longer be assumed to be straight lines since their nanometer-scale variations become a non-negligible fraction of the overall structures' dimensions, rendering the edges “rough”. The 3σ_RMS value of the variations is what is called the Line Edge Roughness. When two rough edges form e.g., a line, its width is also statistically varying, this being known as Line Width Roughness (LWR). The relation between the two is:σLWR=SQRT(2)*σLER 
The foregoing will mean LER, not LWR, when referring to roughness, although both concepts are equally applicable of course. It has been observed that LER has a significant impact on lithography-fabricated devices, in that the more substantial the LER the worse the IC's performance. Moreover, LER is unlikely to scale down at the same rate as the CD does. From these observations it follows that having a shrinking CD (as is the case in every next lithography-generation) and constant LER, the latter becomes a more and more significant fraction of the overall CD error budget. Therefore, the CD control throughout the lithography-process becomes essentially a LER control. Consequently, there is a growing need to be able to determine the LER with sufficient precision.